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https://hdl.handle.net/10784/29295

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Examinando Artículos por Materia "Bifurcation theory"

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    Ítem
    Integration-Free analysis of nonsmooth local dynamics in planar filippov systems
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2009-03-01) Arango, Ivan; Taborda, John Alexander; Arango, Ivan; Taborda, John Alexander; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecatrónica y Diseño de Máquinas
    In this paper, we present a novel method to analyze the behavior of discontinuous piecewise-smooth autonomous systems (denominated Filippov systems) in the planar neighborhood of the discontinuity boundary (DB). The method uses the evaluation of the vector fields on DB to analyze the nonsmooth local dynamics of the Filippov system without the integration of the ODE sets. The method is useful in the detection of nonsmooth bifurcations in Filippov systems. We propose a classification of the points, events and events combinations on DB. This classification is more complete in comparison with the others previously reported. Additional characteristics as flow direction and sliding stability are included explicitly. The lines and the points are characterized with didactic symbols and the exclusive conditions for their existence are based on geometric criterions. Boolean-valued functions are used to formulate the conditions of existence. Different problems are analyzed with the proposed methodology. © 2009 World Scientific Publishing Company.
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    Ítem
    Topological classification of limit cycles of piecewise smooth dynamical systems and its associated Non-Standard Bifurcations
    (Multidisciplinary Digital Publishing Institute (MDPI), 2014-04-01) Alexander Taborda, John; Arango, Ivan; Alexander Taborda, John; Arango, Ivan; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecatrónica y Diseño de Máquinas
    In this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs) in n-dimensional piecewise-smooth dynamical systems, particularly Continuous PWS and Discontinuous PWS (or Filippov-type PWS) systems. The proposed qualitative approach explicitly includes two main aspects: multiple discontinuity boundaries (DBs) in the phase space and multiple intersections between DBs (or corner manifolds-CMs). Previous classifications of DIBs of limit cycles have been restricted to generic cases with a single DB or a single CM. We use the definition of piecewise topological equivalence in order to synthesize all possibilities of nonsmooth limit cycles. Families, groups and subgroups of cycles are defined depending on smoothness zones and discontinuity boundaries (DB) involved. The synthesized cycles are used to define bifurcation patterns when the system is perturbed with parametric changes. Four families of DIBs of limit cycles are defined depending on the properties of the cycles involved. Well-known and novel bifurcations can be classified using this approach. © 2014 by the authors.